You can do it without a puller, but you have to be careful not to bust the lugs where the bolts go through. If you do, then you have to replace that carrier housing.
First thing to do is to drain the lower unit lube, unless you want it everywhere when you pull the unit apart. Set down cardboard anyway, as it's still going to be messy.
After removing the 2 bolts on either side of the prop shaft, use a block of wood and a hammer, and CAREFULLY tap the lug sideways, so as to rotate the carrier housing. Alternate between bottom and top lugs. Once you have it rotated so that the lugs are sideways, once again, VERY CAREFULLY tap on them from the forward side, using a dead blow hammer. This is the part where you have to be careful, or you will break those lugs. Once again, alternate between them, so that you are not causing the carrier housing to be canted as you're trying to remove it.
When the carrier assembly comes out, the prop shaft will also come out with it.
Installation of the carrier during re-assembly is fairly simple. Use a block of wood, drive it back down flush, with the lugs closely aligned. Use the wood block and tap the lugs sideways to align them with bolt holes.